x-24/100x=38

Solution for x-24/100x=38 equation:

x-24/100x=38

We move all terms to the left:

x-24/100x-(38)=0


Domain of the equation: 100x!=0

x!=0/100

x!=0

x∈R


We multiply all the terms by the denominator


x*100x-38*100x-24=0

Wy multiply elements

100x^2-3800x-24=0

a = 100; b = -3800; c = -24;
Δ = b2-4ac
Δ = -38002-4·100·(-24)
Δ = 14449600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14449600}=\sqrt{1600*9031}=\sqrt{1600}*\sqrt{9031}=40\sqrt{9031}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3800)-40\sqrt{9031}}{2*100}=\frac{3800-40\sqrt{9031}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3800)+40\sqrt{9031}}{2*100}=\frac{3800+40\sqrt{9031}}{200}
$